February 23, 2019 February 23, 2019 07:00 AM PST 09:00 AM PST Learn reading strategies that can help even nonvoracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT February 24, 2019 February 24, 2019 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 14 Oct 2014
Posts: 66
Location: United States

If 6/(x(x+1))>1, which of the following could the value of x?
[#permalink]
Show Tags
21 Dec 2014, 15:23
Question Stats:
77% (01:47) correct 23% (01:50) wrong based on 394 sessions
HideShow timer Statistics
If \(\frac{6}{x(x+1)}>1\), which of the following could the value of x? A. 3.5 B. 2.5 C. 2.5 D. 3.5 E. 4.5
Official Answer and Stats are available only to registered users. Register/ Login.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13577
Location: United States (CA)

Re: If 6/(x(x+1))>1, which of the following could the value of x?
[#permalink]
Show Tags
21 Dec 2014, 18:11
Hi viktorija, This question can be solved by TESTing THE ANSWERS. One (and only one) or those numbers could be a solution to the given inequality, so we could check them (just plug them in) until we find one that "fits" the given inequality. There is a logical math shortcut here though that we can take advantage of: We're told that 6/(product) > 1 so the denominator must be LESS than 6. That way 6/(less than 6) will be > 1. So we're really just looking for a product that's less than 6. Logically, we're probably looking for a value for X that's relatively close to 0, so let's check answers B and C....But don't do the math just yet... Answer B: X = 2.5 Denominator = (2.5)(1.5) Answer C: X = 2.5 Denominator = (2.5)(3.5) Since the negative signs will cancel out in Answer B, you don't have to do the math to see that Answer B is smaller. Since there's only one answer that will "fit", it has to be B. Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



Director
Joined: 07 Aug 2011
Posts: 529
Concentration: International Business, Technology

Re: If 6/(x(x+1))>1, which of the following could the value of x?
[#permalink]
Show Tags
10 Jan 2015, 01:19
If 6/(x(x+1))>1, which of the following could the value of x? A.3.5 B.2.5 C.2.5 D.3.5 E.4.5 Given 6/(x(x+1))>1 i.e x(x+1) is +ive implies X is positive ; since we are dealing with all positives 6/(x(x+1))>1 > (x+3)(x2)<0 ++++++(3)(2)++++++ so anything between 3 and 2 satisfies the inequality . B. 2.5 Bunuel am i doing right ?



Manager
Joined: 02 May 2014
Posts: 96

Re: If 6/(x(x+1))>1, which of the following could the value of x?
[#permalink]
Show Tags
10 Jan 2015, 03:26
Lucky2783 wrote: If 6/(x(x+1))>1, which of the following could the value of x? A.3.5 B.2.5 C.2.5 D.3.5 E.4.5 Given 6/(x(x+1))>1 i.e x(x+1) is +ive implies X is positive ; since we are dealing with all positives 6/(x(x+1))>1 > (x+3)(x2)<0 ++++++(3)(2)++++++ so anything between 3 and 2 satisfies the inequality . B. 2.5 Bunuel am i doing right ? Lucky2783 ,I don't think this derivation of yours is right: x(x+1) is +ive implies X is positive. Please check!



Senior Manager
Joined: 13 Jun 2013
Posts: 275

Re: If 6/(x(x+1))>1, which of the following could the value of x?
[#permalink]
Show Tags
10 Jan 2015, 05:01
viktorija wrote: If 6/(x(x+1))>1, which of the following could the value of x?
A.3.5 B.2.5 C.2.5 D.3.5 E.4.5 \(\frac{6}{x(x+1)} >1\) let's analyze the denominator. x(x+1) = x^2+x. now x^2+x will always be positive except for numbers lying between 1 and 0. now if x lies between 1 and 0, then the fraction \(\frac{6}{x(x+1)}\) will be negative. this violates our initial given condition that \(\frac{6}{x(x+1)} >1\). hence the expression x^2+x will always be positive. now since expression x^2+x is positive, therefore we can cross multiply. Thus we have x^2+x<6 x^2+x6<0 (x+3)(x2)<0 now for all values of x which are less than 3, (x+3)(x2) will always be positive. similarly for all values of x , which are greater than 2, (x+3)(x2) will always be positive. hence our desired range is between 3 and 2. i.e. 3<x<2. now out of the given options, only option b lies inside this range. hence answer must be B



Director
Joined: 07 Aug 2011
Posts: 529
Concentration: International Business, Technology

Re: If 6/(x(x+1))>1, which of the following could the value of x?
[#permalink]
Show Tags
10 Jan 2015, 05:46
sytabish wrote: Lucky2783 wrote: If 6/(x(x+1))>1, which of the following could the value of x? A.3.5 B.2.5 C.2.5 D.3.5 E.4.5 Given 6/(x(x+1))>1 i.e x(x+1) is +ive implies X is positive ; since we are dealing with all positives 6/(x(x+1))>1 > (x+3)(x2)<0 ++++++(3)(2)++++++ so anything between 3 and 2 satisfies the inequality . B. 2.5 Bunuel am i doing right ? Lucky2783 ,I don't think this derivation of yours is right: x(x+1) is +ive implies X is positive. Please check! thanks . actually we do not need know the sign of X here Given 6/(x(x+1))>1 implies (x(x+1)) is a +ive quantity so we can simply multilply both sides of inequality by (x(x+1)) 6 > (x(x+1)) 6> x^2 + x x^2+x6 < 0 (x+3)(x2)<0 ++++++(3)(2)++++++ so anything between 3 and 2 satisfies the inequality . B. 2.5



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13577
Location: United States (CA)

Re: If 6/(x(x+1))>1, which of the following could the value of x?
[#permalink]
Show Tags
10 Jan 2015, 12:37
Hi styabish, You have to be very careful with your assumptions in the Quant section. This specific Number Property WILL show up on Test Day.... (X)(X+1) = positive This does NOT mean that X has to be positive. X COULD be positive.... eg X = 1 (1)(2) = 2 X COULD be NEGATIVE though... eg X = 2 (2)(1) = 2 GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1820
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: If 6/(x(x+1))>1, which of the following could the value of x?
[#permalink]
Show Tags
12 Jan 2015, 20:56
\(\frac{6}{(x(x+1))} > 1\) \(\frac{6}{x^2 + x} > 1\) For x = 3.5 \(\frac{6}{12.253.5}\) >> This would be less than 1 For x = 2.5 \(\frac{6}{6.252.5}\) >> This would be greater than 1 Answer = B
_________________
Kindly press "+1 Kudos" to appreciate



Intern
Joined: 22 Mar 2015
Posts: 4

Re: If 6/(x(x+1))>1, which of the following could the value of x?
[#permalink]
Show Tags
21 Aug 2015, 07:27
viktorija wrote: If 6/(x(x+1))>1, which of the following could the value of x?
A.3.5 B.2.5 C.2.5 D.3.5 E.4.5 isn't this what you get after factorising x<3 or x<2 then how is 2.5 the answer? (since 2.5 is greater than 3) Can someone help, please?



Math Expert
Joined: 02 Sep 2009
Posts: 53066

Re: If 6/(x(x+1))>1, which of the following could the value of x?
[#permalink]
Show Tags
21 Aug 2015, 07:36



CEO
Joined: 20 Mar 2014
Posts: 2629
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: If 6/(x(x+1))>1, which of the following could the value of x?
[#permalink]
Show Tags
21 Aug 2015, 07:41
aggarwalpooja wrote: viktorija wrote: If 6/(x(x+1))>1, which of the following could the value of x?
A.3.5 B.2.5 C.2.5 D.3.5 E.4.5 isn't this what you get after factorising x<3 or x<2then how is 2.5 the answer? (since 2.5 is greater than 3) Can someone help, please? The most straightforward method for this type of question will be to use the values in the options and see which one gives you >1 . Only 1 option must satisfy this requirement. Additionally, for algebraic solution, look below: Given : \(\frac{6}{x(x+1)} > 1\) > \(\frac{6}{x(x+1)}  1 > 0\) > \(\frac{6x^2x}{x(x+1)} > 0\) > \(\frac{6+x^2+x}{x(x+1)} < 0\) \(\frac{(x+3)(x2)}{x(x+1)} < 0\) > 3<x<1 or 0<x<2 Only 2.5 lies in this range. Hope this helps.



Intern
Joined: 22 Mar 2015
Posts: 4

Re: If 6/(x(x+1))>1, which of the following could the value of x?
[#permalink]
Show Tags
Updated on: 27 Aug 2015, 01:19
Bunuel wrote: aggarwalpooja wrote: viktorija wrote: If 6/(x(x+1))>1, which of the following could the value of x?
A.3.5 B.2.5 C.2.5 D.3.5 E.4.5 isn't this what you get after factorising x<3 or x<2 then how is 2.5 the answer? (since 2.5 is greater than 3) Can someone help, please? Let me ask you: what does x < 3 (x is less than 3) or x < 2 (x is less than 2) even mean? As for the solution please see above. This link sorted my worries! For anyone who struggled in the last bit after factorising refer this: https://www.khanacademy.org/math/algebr ... equalitiesThanks Bunuel! Now I know why did you ask me what didx < 3 (x is less than 3) or x < 2 (x is less than 2) even mean?
Originally posted by aggarwalpooja on 21 Aug 2015, 07:58.
Last edited by aggarwalpooja on 27 Aug 2015, 01:19, edited 1 time in total.



Intern
Joined: 22 Mar 2015
Posts: 4

Re: If 6/(x(x+1))>1, which of the following could the value of x?
[#permalink]
Show Tags
21 Aug 2015, 08:15
Engr2012 wrote: aggarwalpooja wrote: viktorija wrote: If 6/(x(x+1))>1, which of the following could the value of x?
A.3.5 B.2.5 C.2.5 D.3.5 E.4.5 isn't this what you get after factorising x<3 or x<2then how is 2.5 the answer? (since 2.5 is greater than 3) Can someone help, please? The most straightforward method for this type of question will be to use the values in the options and see which one gives you >1 . Only 1 option must satisfy this requirement. Additionally, for algebraic solution, look below: Given : \(\frac{6}{x(x+1)} > 1\) > \(\frac{6}{x(x+1)}  1 > 0\) > \(\frac{6x^2x}{x(x+1)} > 0\) > \(\frac{6+x^2+x}{x(x+1)} < 0\) \(\frac{(x+3)(x2)}{x(x+1)} < 0\) > 3<x<1 or 0<x<2 Only 2.5 lies in this range. Hope this helps. Thanks Engr12, plugging in the value is guess the easiest!



Manager
Joined: 25 Mar 2013
Posts: 239
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5

Re: If 6/(x(x+1))>1, which of the following could the value of x?
[#permalink]
Show Tags
02 Jan 2017, 12:43
\(\frac{6}{(x(x+1))} > 1\) 6 > x(x+1) \(6 > x^{2} + x\) Plug In options B
_________________
I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you



VP
Joined: 09 Mar 2016
Posts: 1284

Re: If 6/(x(x+1))>1, which of the following could the value of x?
[#permalink]
Show Tags
20 Feb 2018, 10:10
Lucky2783 wrote: sytabish wrote: Lucky2783 wrote: If 6/(x(x+1))>1, which of the following could the value of x? A.3.5 B.2.5 C.2.5 D.3.5 E.4.5 Given 6/(x(x+1))>1 i.e x(x+1) is +ive implies X is positive ; since we are dealing with all positives 6/(x(x+1))>1 > (x+3)(x2)<0 ++++++(3)(2)++++++ so anything between 3 and 2 satisfies the inequality . B. 2.5 Bunuel am i doing right ? Lucky2783 ,I don't think this derivation of yours is right: x(x+1) is +ive implies X is positive. Please check! thanks . actually we do not need know the sign of X here Given 6/(x(x+1))>1 implies (x(x+1)) is a +ive quantity so we can simply multilply both sides of inequality by (x(x+1)) 6 > (x(x+1)) 6> x^2 + x x^2+x6 < 0 (x+3)(x2)<0 ++++++(3)(2)++++++ so anything between 3 and 2 satisfies the inequality . B. 2.5 hello there! How did you manage to draw the line based on this (x+3)(x2)<0 is there rule to transform it into line ? thank you



Manager
Joined: 10 Apr 2018
Posts: 183

Re: If 6/(x(x+1))>1, which of the following could the value of x?
[#permalink]
Show Tags
13 Sep 2018, 15:24
Hi dave13, Let me try to respond to your query. If \(\frac{6}{x(x+1)}\)>1, which of the following could the value of x? note x and (x+1) are two consecutive numbers, then their product is always positive . Why if x is negative then (x+1) is also negative and their product is always positive if x is positive then (x+1) is also positive and their product is always positive But x cannot be 1 and 0 , because the exp will be undefined for these values. So we can write \(\frac{6}{x(x+1)}\)>1 as \(\frac{6}{x(x+1)}\)1>0 So \(\frac{(6x(x+1)}{x(x+1)}\)>0 \(\frac{(6x^2x)}{x(x+1)}\)>0 \(\frac{((x+3)(x2))}{x(x+1)}\)>0 When we multiply by 1 on both sides we change the sign of inequality. \(\frac{((x+3)(x2))}{x(x+1)}\)<0 Now if you draw the number line and have positive and negative regions this is how it would look ++++++++++++(3)(1)++++++++++++(0)(2)++++++++++ Now the region where the inequality holds is 3<x<1 and 0<x<2 Now options B, C, D are greater than 2 so discard. Option A is less than 3 so discard Option B lies between 3<x<1 so this could be possible value of for which the inequality will hold. Probus



VP
Status: It's near  I can see.
Joined: 13 Apr 2013
Posts: 1405
Location: India
Concentration: International Business, Operations
GPA: 3.01
WE: Engineering (Real Estate)

Re: If 6/(x(x+1))>1, which of the following could the value of x?
[#permalink]
Show Tags
14 Sep 2018, 05:09
viktorija wrote: If 6/(x(x+1))>1, which of the following could the value of x?
A.3.5 B.2.5 C.2.5 D.3.5 E.4.5 \(\frac{6}{[x (x + 1)]}\)\(> 1\) \(\frac{6}{[x^2 + x]}\) > 1 We know that \(x^2 + x\) can never be negative irrespective of the value of \("x"\), therefore \(6 > x^2 + x\) Or \(x^2 + x  6 < 0\) \((x + 3) (x  2) < 0\) \((x  2) < 0\) or \((x + 3) > 0\) \(x < 2\) or \(x > 3\) \(3 < x < 2\) Answer : B = \(2.5\)
_________________
"Do not watch clock; Do what it does. KEEP GOING."




Re: If 6/(x(x+1))>1, which of the following could the value of x?
[#permalink]
14 Sep 2018, 05:09






